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2D dynamic analysis of the disturbances in the calcium neuronal model and its implications in neurodegenerative disease

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Abstract

Ca2+ signaling is an essential function of neurons to control synaptic activity, memory formation, fertilization, proliferation, etc. Protein and voltage-dependent calcium channels (VDCCs) maintain an adequate level of calcium concentration ([Ca2+]). An alteration in [Ca2+] leads to the death of the neurons that start the primary symptoms of the disease. The present study deals with cell memory-based mathematical modeling of Ca2+ that is characterized by the presence of protein and VDCC. We developed a two-dimensional Ca2+ neuronal model to study the spatiotemporal behavior of the Ca2+ profile. All principal parameters like buffer concentration, diffusion coefficient, VDCC fluxes, etc. are incorporated in this model. Apposite initial and boundary conditions are applied to the physiology of the problem. We obtained an approximate Ca2+ profile by the fractional integral transform method. The application of obtained results is performed to provide its implications to estimate the [Ca2+] in neurodegenerative disease. It is observed that the protein and VDCC provide a significant impact in the presence of cell memory. The memory of cells shrinks the Ca2+ flow from elevation and provides better results to estimated Ca2+ flow in the disease state.

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No funding to declare. The authors are thankful to the editor and anonymous reviewers for their constructive comments and suggestions to improve the quality and presentation of the manuscript.

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  1. Department of Mathematics, LJ Institute of Engineering and Technology, LJ University, Ahmedabad, 382210, India

    Hardik Joshi

  2. Department of Mathematics, School of Technology, Pandit Deendayal Energy University, Gandhinagar, 382007, India

    Brajesh Kumar Jha

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  1. Hardik Joshi
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  2. Brajesh Kumar Jha
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Joshi, H., Jha, B.K. 2D dynamic analysis of the disturbances in the calcium neuronal model and its implications in neurodegenerative disease. Cogn Neurodyn 17, 1637–1648 (2023). https://doi.org/10.1007/s11571-022-09903-1

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